Consider the function . the slope of the tangent line to f(x) at is . the value of f(x) at is . the y-intercept of the tangent line at is .

We know that first derivative gives the slope of the given equation.

First derivative of the given function is given by formula d/dx(x^n)=nx^(n-1)

so first derivative will be

now to find the slope at x=-9, plug it into above equation

Hence slope of tangent at x=-9 is 45.

----------------

To find the value of f(x) at x=-9 we just plug x=-9 into given equation.

Hence value of f(x) at x=-9 is f(-9)=-333.

----------------------------

To find y-intercept of the tangent line, first we need to find the equation of tangent line.

at x=-9, we got f(x)=-333 so that means tangent line passes through point (-9,-333)

we also know slope of tangent is m=45

now plug those values into formula y=mx+b

-333=45(-9)+b

-333=-405+b

-333+405=b

72=b

In y=mx+b, b shows y-intercept.

Hence required y-intercept of the tangent line at x=-9 is 72.

i wish i could you, i have no idea how to answer this

step-by-step explanation:

answer: list the statements and i will follow up!

step-by-step explanation: