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
 Math (equation of tangent line)  Consider the implicit equation 2xy1=(x+y+1)^2...
 Calculus  If F(x)=x^3−7x+5, use the limit definition of the derivative to...
 Calculus  1. a) For the Function and point below , Find f’(a). b) Determine the...
 Calculus  1. a) For the Function and point below , Find f’(a). b) Determine the...
 calculus  1. Which of the following expressions is the definition of the ...
 Calculus  Using the definition of the derivative, find the equation of the ...
 Derivative Calculus  I just need my answers checked. 1) Find the derivative. f(...
 Math (Calculus) (mean value theorem emergency)  Consider the graph of the ...
 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) ...
More Related Questions