What are the maximum and minimum values of f(x)= -4x+3 on the interval [-1,6]?
Well, let me tell you a little joke first. Why don't scientists trust atoms? Because they make up everything!
Now, let's solve the problem with a smile. To find the maximum and minimum values of f(x)= -4x+3 on the interval [-1,6], we can start by plugging in the endpoints of the interval and see what we get.
When we substitute x = -1 into f(x), we get f(-1) = -4(-1) + 3 = 7.
When we substitute x = 6 into f(x), we get f(6) = -4(6) + 3 = -21.
So, the maximum value is 7 and the minimum value is -21. Keep smiling and keep on solving those problems!
To find the maximum and minimum values of the function f(x) = -4x + 3 on the interval [-1, 6], we need to evaluate the function at the endpoints and critical points within the interval.
Step 1: Evaluate f(x) at the endpoints.
- Evaluate f(x) at x = -1:
f(-1) = -4(-1) + 3 = 4 + 3 = 7
- Evaluate f(x) at x = 6:
f(6) = -4(6) + 3 = -24 + 3 = -21
Step 2: Find critical points.
To find the critical points of the function, we need to find where the derivative of the function is equal to zero.
- Find the derivative of f(x):
f'(x) = -4
- Set f'(x) = 0 and solve for x:
-4 = 0
Since there is no solution for this equation, there are no critical points.
Step 3: Compare the values found.
From Step 1, we found that f(x) = 7 at x = -1 and f(x) = -21 at x = 6.
Therefore, the maximum value is 7, and the minimum value is -21 for the function f(x) = -4x + 3 on the interval [-1, 6].
To find the maximum and minimum values of the function f(x) = -4x + 3 on the interval [-1, 6], we can start by identifying the critical points within this interval.
The critical points occur where the derivative of the function is equal to zero or does not exist. Since f(x) = -4x + 3 is a linear function, its derivative is a constant, which is -4 in this case. Since -4 is always nonzero, the derivative is never equal to zero. Therefore, there are no critical points within the interval [-1, 6].
Next, we need to evaluate the function f(x) at the endpoints of the interval.
When x = -1:
f(-1) = -4(-1) + 3 = 4 + 3 = 7
When x = 6:
f(6) = -4(6) + 3 = -24 + 3 = -21
Therefore, the maximum value of f(x) = -4x + 3 on the interval [-1, 6] is 7, and the minimum value is -21.
That is a straight line with slope of -4
so look at the two ends
-4(-1) +3
-4(6) +3