need tangent line immediately please

Question

Let: f(x) = 5x^3 + 13x - 3

The derivative function is: f ' (x) = ((5(x+h)^2 + 13(x+h) - 3) - (5x^2 + 13x - 3)) / h

The f ' (x) = df/dx = 10x + 13

Based on this information, I need to find the tangent line for f(x) where x = 2. Can someone please help me find this? I need immediate help please.

I think the equation would be y = 33(2) + b, but I'm not sure if this equation is right, and if this equation is right, I don't know what b would be.

Please help me find the tangent line!

Answer 1

f'(x) = 15x² + 13 Check you arithmetic.

f'(2) = 43

f(2) = 5(8) + 13(2) - 3

f(2) = 63

Point is (2, 63) and slope is 43

Use point-slope form to determine equation.

y = 33x - 3