
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.
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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.
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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.