Respuesta :
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
Step-by-step 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
Answer:
a) x = 5
b) x = 2
Step-by-step explanation:
The given function is f(x) = x² - 10x + 6 and we want to find the values of x such that slope of the curve equals to 0 and -6. This can be done by taking the derivative of the function f(x) and setting that equal to 0 and -6 respectively.
When slope of curve = 0
Take the derivative of the function f(x)
f(x) = x² - 10x + 6
f'(x) = 2x - 10 + 0
f'(x) = 2x - 10
Now put f'(x) = 0
0 = 2x - 10
2x = 10
x = 10/2 = 5
Hence x = 5
When slope of curve = -6
We have already taken the derivative so we just have to put f'(x) = -6
-6 = 2x - 10
2x = -6 + 10
2x = 4
x = 4/2 = 2
Hence x = 2
