33. Exercises 25 − 36 refer to Fig. 23 , which contains the graph of f ' ( x ) the derivative of function f ( x ) . If f ( 6 ) = 3 , what is the equation of the tangent line to the graph of y = f ( x ) at x = 6 ?
33. Exercises 25 − 36 refer to Fig. 23 , which contains the graph of f ' ( x ) the derivative of function f ( x ) . If f ( 6 ) = 3 , what is the equation of the tangent line to the graph of y = f ( x ) at x = 6 ?
Solution Summary: The author explains that the equation of the tangent line is y-3=2(x-6).
4. Suppose that the population of a certain collection of rare Brazilian ants is given by
P(t)=(t+100) In(t+2),
Where t represents the time in days. Find and interpret the rates of change of the population on the third day
and on the tenth day.
Find all values of x for f (x)=(x²-4) 4 where the tangent line is horizontal.
5. Find the slope of the tangent line to the graph of f(x)=-√8x+1 at x=1. Write the equation of the tangent
line.
3. Find the derivative of each function. Label with appropriate derivative notation showing both dependent and
independent variables.
f(t)=4t(2t⭑+4)³
a. f(t)=4t (2t+4)³ (Answer must be factored.)
b.
y=
3
1
(2x³-4)
6
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