If f(x) = 6x^2 - x^3, find f?'(1) and use it to find an equation of the tangent line to the curve y = 6x^2 - x^3 at the point (1, 5).

Question

I am so lost please help

Answer 1

f(x)=6x^2-x^3

find the first derivative

y=6x^2-x^3

dy/dx=12x-3x^2

 

calculate the gradient of the tangent at the point (1,5); substitute the x-value into the equation for the derivative

dy/dx=12(1)-3(1^2)

therefore m=12-3=9

 

determine the equation of the tangent by substituting the gradient and the coordinates of the point into the gradient-point form

y-y1=m(x-x1)

y-5=9(x-1)

y-5=9x-9

y=9x-9+5

y=9x-4