Question

Using the limit derivative of the derivative to find the slope of the tangent line to curve f(x)=4x^2 at x=3, what is f(3+h)?

Answer 1

`f(x)=4x^2`
`f^(\prime)(x)=8x`
`f^(\prime)(x=3)=8\cdot3=24`

the slope at x=3 is 24

for f(3+h)

`f(3+h)=4(3+h)^2`
`f(3+h)=4(9+2\cdot3\cdot h+h^2)`
`f(3+h)=36+24h+h^2`