Let f (x )equals x squared minus 10 x plus 6. a. Find the values of x for which the slope of the curve yequalsf(x) is 0. b. Find the values of x for which the slope of the curve yequalsf(x) is negative 6.

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

answer for #1 is c

answer for #2 is d

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