Find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1) and the xaxis.
I don't really get what this question is asking.
It looks like the area of right triangle to me...try the graph, and shade the area under the tangent.
Find out where the tangent line crosses the xaxis. Then draw yourself a figure to see what area they are talking about. The tangent line will intersect the x axis at some x value that is >0. I would suggest doing this by calculating the area under the y = x^2 curve and the x axis from x=0 to x=1, using a simple integral from 0 to 1 of y(x), and subtracting the triangular area formed by the tangent line, x=1 and the x axis.
Please ignore the "#1 of 2" in my name. There is aome problem with the Jiskha software automatically entering my name wrong when I prepare answers
i need a refresher on how to find the tangent line. thanks.
The first derivative of a function evaluated at the point will give the slope of the line tangent to the function there. Since you know the point and the slope you can determine the equation for the line.
Briefly
m=f'(x_o) at (x_o,f(x_o)) and the equation for the tangent line is
yf(x_o)=f'(x_o)(xx_o)
where (x_o,f(x_o)) is any point where f(x) is defined.
ok. I found the equation to be y=2x1. I draw the diagram but i am not sure which area i am suppose to find. The triangle under the tangent line and the xaxis??
 👍
 👎
 👁
 ℹ️
 🚩
Answer this Question
Related Questions

math
Draw a diagram to show that there are two tangent lines to the parabola y = x2 that pass through the point (0, −25). Find the coordinates of the points where these tangent lines intersect the parabola.
 asked by Kyle
 6,550 views

Tangent problem
For what values of a and b is the line 2x + y = b tangent to the parabola y = ax2 when x = 5?
 asked by Michael
 5,623 views

calculus
Find the volume of the solid obtained by rotating the region bounded by the curves y = x^8, y = 1 about the line y = 5.
 asked by maggie
 5,929 views

Math
Consider the graph of the parabola f(x)equals=x squaredx2. For xgreater than>0 and hgreater than>0, the secant line through (x,f(x)) and (xplus+h,f(x+h)) always has a greater slope than the tangent line at (x,f(x)). Choose the correct
 asked by Ashley
 3,694 views

Calculus please help
Find the centroid of the area bounded by the parabola y=4x^2 and the xaxis A.(0,1.6) B.(0,1.7) C.(0,1.8) D.(0,1.9)
 asked by Tracy
 6,202 views

math
Consider the parabola y = 6x − x2. (a) Find the slope of the tangent line to the parabola at the point (1, 5). 4 (b) Find an equation of the tangent line in part (a). y =
 asked by Yuxiang Nie
 2,520 views

calculus
Find the area of region bounded by the curves y=sin(pi/2*x)and y=x^22x.
 asked by Liz
 2,213 views

Calculus
Find the volume of the solid obtained by rotating the region bounded by the curves y=cos(x), y=0, x=0, and x=π/2 about the line y=1.
 asked by Ayaka
 3,602 views

K
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 3e^(x), y = 3, x = 2; about y = 6
 asked by Gagan
 2,300 views

Calculus
Find the area of the region bounded by the curves y = sin x, y = csc^2x, x = pi/4, and x = (3pi)/4.
 asked by Slaya
 2,874 views

Calculus Help Please Urgent!!!
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x^2, y = 5x, x ≥ 0; about the xaxis V = ??? Sketch the region
 asked by Top
 1,229 views

Calculus
Find the area of the region bounded by the curves y = x^(1/2), y = x^(–2), y = 1, and y = 3. a) (1/2)(3)^1/2 + (4/3) b) 2*(3)^1/2  (8/3) c) (1/2)(3)^1/2  (32/3) d) 2*(3)^1/2  (32/3) e) (8/3)  2*(3)^1/2 So one thing that is throwing me off on this
 asked by Emily
 1,945 views

Calculus AB: Area Between Curves
Hello! I'm having trouble understanding how I'm supposed to work out this problem. Any help would be appreciated! Find the area of the region bounded by the curve y = f(x) = x3 – 4x + 1 and the tangent line to the curve y = f(x) at (–1,4).
 asked by Pax
 872 views

calculus 2
Find the area of the region bounded by the parabola y = 3x^2, the tangent line to this parabola at (1, 3), and the xaxis.
 asked by TayB
 6,033 views

Calc 2
Find the area of the region bounded by the parabola y = 5x2, the tangent line to this parabola at (5, 125), and the xaxis. its not 625/3
 asked by steve
 2,824 views

calculus
Find the exact area of the region bounded by the axis and the graph of (x^3)x
 asked by cw
 2,295 views

Calculus Please Help
1. A particle moves along the xaxis in such a way that it's position in time t for t is greater or equal to 0 is given by x= 1/3t^3  3t^2 +8t A. Find the position of the particle at time t = 3. B. Show that at time t = 0, the particle is moving to the
 asked by Sarah
 688 views

maths
Find parametric equations of the line that is tangent to the parabola y = x^2 at the point (−2, 4).
 asked by ramesh
 1,700 views

Calculus
1. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6. y = x, y = 0, y = 5, x = 6 2. Use the method of cylindrical shells to find the volume V generated by rotating the region bounded
 asked by Mark
 1,427 views

Calculus
1. Consider the curve y = f(x) = 2^x  1. A. Find the exact area of the region in the first quadrant bounded by the curves y = f(x) = 2^x  1 and y = x. ("Exact area" means no calculator numbers.) B. Find the inverse function y = f^1 (x). C. Using part A
 asked by KingS.
 1,156 views
Still need help?
You can ask a new question or browse existing questions.