Find the slope of the curve
y = 2x2 + 5x−3 at (1,4)
A. 4
B. 0
C. 7
D. 9
To find the slope of the curve, we need to take the derivative of the equation y = 2x^2 + 5x - 3.
Taking the derivative with respect to x, we get:
dy/dx = 4x + 5
To find the slope at the point (1,4), we substitute x = 1 into the derivative:
dy/dx = 4(1) + 5 = 4 + 5 = 9
Therefore, the slope of the curve at (1,4) is 9.
The correct answer choice is D. 9.
To find the slope of the curve at a specific point, we need to find the derivative of the function and evaluate it at that point.
The given function is y = 2x^2 + 5x - 3.
We will differentiate this function with respect to x to find the derivative. The derivative represents the slope of the tangent line to the curve at any given point.
Differentiating y = 2x^2 + 5x - 3, we get:
dy/dx = 4x + 5
Now we need to evaluate the derivative at the point (1,4).
Substitute x = 1 into the derivative equation:
dy/dx = 4(1) + 5 = 9
Therefore, the slope of the curve at the point (1,4) is 9.
The correct answer is D. 9.