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

## Answer this Question

## Related Questions

- Calculus - If F(x)=x^3−7x+5, use the limit definition of the derivative to...
- calculus - 1. Which of the following expressions is the definition of the ...
- Derivative Calculus - I just need my answers checked. 1) Find the derivative. f(...
- Calculus - I am not sure what to do here: Find the derivative (f '(x) using the ...
- ap calculus ab - for f(x)=lnx we know that f(e)=1. Use the tangent line at(e,1) ...
- Calculus - 1. a) For the Function and point below , Find f’(a). b) Determine ...
- Calculus - 1. a) For the Function and point below , Find f’(a). b) Determine ...
- HS Calculus - Definition of the derivative to calculate f'(x) if f(x) = square ...
- calculus - 1. Which of the following expressions is the definition of the ...
- Math- Calculus - Find an equation of the line that is tangent to the graph of f ...