# Math Help - slope of tangent line at point (4,f(4))

1. ## slope of tangent line at point (4,f(4))

Consider the function f(x) = 3x^(3)-5x^(2)-6
a) find [f(x+h) - f(x)]/h
(I found: 9x^2 + 9xh+3h^2-10x-5h, which is correct)
b) Find the derivative of f at x
(I found: 9x^2 - 10x, which is correct as well)

***c)What is the slope of the tangent line to the graph of f at the point (4,f(4))?

I don't know where to sub in these values, i tried substituting x=4 and y=4 into f(x) = 3x^(3)-5x^(2)-6 as well as 9x^2 + 9xh+3h^2-10x-5h to get the slope but in all honesty i don't have a clue
what is the "slope of tangent line" equation? i thought it was [f(x+h) - f(x)]/h as h approaches 0-- yes? no?

thanks
Brittany

2. Originally Posted by williamb
Consider the function f(x) = 3x^(3)-5x^(2)-6
a) find [f(x+h) - f(x)]/h
(I found: 9x^2 + 9xh+3h^2-10x-5h, which is correct)
b) Find the derivative of f at x
(I found: 9x^2 - 10x, which is correct as well)

***c)What is the slope of the tangent line to the graph of f at the point (4,f(4))?

I don't know where to sub in these values, i tried substituting x=4 and y=4 into f(x) = 3x^(3)-5x^(2)-6 as well as 9x^2 + 9xh+3h^2-10x-5h to get the slope but in all honesty i don't have a clue
what is the "slope of tangent line" equation? i thought it was [f(x+h) - f(x)]/h as h approaches 0-- yes? no?

$f'(x)=9x^2 - 10x$ so
$f'(4)=9(4)^2 - 10(4)=144-40=104$