Derivatives, Sin and Cos, Rate of Change, Tangent Lines

[JackieAnne]

Hi, I am in calculus and am having major struggles. If someone could provide a walk through on how to answer these questions, that would be fantastic. Cheers!

Let f(x)=−3x+6 if x<-3
= 15 if x > -3

Find the average rate of change of f(x) on the interval −5<x<5 .

The average rate of change of f(x) on the interval −5<x<5 is ?


Consider the function f(x)=−7/x+4.

We will take steps to find the tangent line to the graph of f at the point (−7,−3/−7).

(a) Let (xf(x)) be a point on the graph of f with x=−7 . The slope of the (secant) line joining the two points (−7,−3/−7) and (xf(x)) can be simplified to the form A/x+4, where A is a constant. Find A.

Answer: A= .

(b) By considering the slope of the secant line as x approaches −7, find the slope of the tangent line to the graph of f at the point (−7,−3/−7).

Answer: The slope of the tangent line to the graph of f at the point (−7,−3/−7) is .

(c) Find the equation of the tangent line to the graph of f at the point (−7,−3/−7). Write your answer in the form y=mx+b.

 

[Je m'appelle]

You have to provide us with a step by step attempt at a solution, so we can try to help you where you're struggling. Nobody is going to solve your homework, this is not the point of this forum. We're homework helpers not solvers.

 

[Mark44]

Hi, I am in calculus and am having major struggles. If someone could provide a walk through on how to answer these questions, that would be fantastic. Cheers!

Let f(x)=−3x+6 if x<-3
= 15 if x > -3

Find the average rate of change of f(x) on the interval −5<x<5 .

The average rate of change of f(x) on the interval −5<x<5 is ?


Consider the function f(x)=−7/x+4.

We will take steps to find the tangent line to the graph of f at the point (−7,−3/−7).

(a) Let (xf(x)) be a point on the graph of f with x=−7 . The slope of the (secant) line joining the two points (−7,−3/−7) and (xf(x)) can be simplified to the form A/x+4, where A is a constant. Find A.

Answer: A= .

(b) By considering the slope of the secant line as x approaches −7, find the slope of the tangent line to the graph of f at the point (−7,−3/−7).

Answer: The slope of the tangent line to the graph of f at the point (−7,−3/−7) is .

(c) Find the equation of the tangent line to the graph of f at the point (−7,−3/−7). Write your answer in the form y=mx+b.

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