The question is:
Let f(x) = x² - 10x + 6
a. Find the values of x for which the slope of the curve y = f(x) is 0.
b. Find the values of x for which the slope of the curve y = f(x) is -6.
Answer:
(a) The value of x for which the slope is 0 is 5
(b) The value of x for which the slope is -6 is 2
Explanation:
Given y = f(x) = x² - 10x + 6
The Slope is given as dy/dx = f'(x)
It is obtained by differentiating y = f(x) once with respect to x.
Let us find the first derivative of
y = x² - 10x + 6
That is
dy/dx = 2x - 10
Now
(a) We want to find the value of x for which the slope dy/dx = 0
We set
2x - 10 = 0
And solve for x, to have
2x = 10
x = 10/2 = 5
(b) The value of x for which the slope is -6
We set
2x - 10 = -6
2x = -6 + 10 = 4
x = 4/2 = 2