Posted by **Irene** on Monday, June 14, 2010 at 3:35pm.

Consider the function.

f (x) = 5x3 + 3x

(a) Compute the derivative at x = 3 using the limit definition.

f '(3) =

(b) Find an equation of the tangent line.

2

- calculus -
**Reiny**, Monday, June 14, 2010 at 5:07pm
evaluate f(3)

evaluate (3+h) and simplify

then take

Limit [ (f(3+h) - f(3) ]/h as h --->0

You should be able to factor out an h from the top which would then cancel the h in the bottom

you should get

f'(3) = 138

b) when x=3, y = 138 (that's a coincidence)

so you have

slope of tangent is 138 and (3,138) is a point on it

y = 138x + b , plug in the point

138 = 138(3) + b

b = -276

so y = 138x - 276 is the tangent equation

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