Find the slope m of the tangent line to the parabola f(x)=x2+2x at the point (4, 24) by using the definition:
m=limh→0f(a+h)−f(a)/(h)

m=

Find the equation for the tangent line at the point (4, 24), and write it in the form y=mx+b
y
=
m
x
+
b
where
m = and
b =

Question

Find the slope m of the tangent line to the parabola f(x)=x2+2x at the point (4, 24) by using the definition:
m=limh→0f(a+h)−f(a)/(h)

m=
  
Find the equation for the tangent line at the point (4, 24), and write it in the form y=mx+b
y
=
m
x
+
b
 where 
m =       and 
b =

mathmale · Answer

First:  some housekeeping:  Please express exponentiation using the symbol " ^ ."

Unclear:  f(x)=x2+2x
Clear:      f(x)=x^2+2x

mathmale · Answer

Definition of derivative:

f'(x)= (limit as h approaches zero) of $$\frac{ f(x+h)-f(x) }{ h }$$

mathmale · Answer

What is f(x+h)?  Write out all terms.
What is f(x+h)-f(x)?  Simplifly your result.

What is $$\frac{ f(x+h)-f(x) }{ h }$$

mathmale · Answer

After all possible simplifications, let h approach zero.

Be sure to label your result with f '(x).