Question

Let f(x) = 5x5 - 5x³ +7. Find the equation of the line tangent to the graph of y = f(x) at the

point (2,127).
The equation of the tangent line is y =

Answer 1

y = 340x - 553

Explanation:

`f(x)=5x^5-5x^3+7\\f'(x)=25x^4-15x^2`

Find the slope of the tangent line at x=2

`f'(2)=25(2)^4-15(2)^2\\f'(2)=25(16)-15(4)\\f'(2)=400-60\\f'(2)=340`

Use point-slope form to create the tangent line

`y-y_1=m(x-x_1)\\y-127=340(x-2)\\y-127=340x-680\\y=340x-553`