Calculus Question

Question

Use a calculator to approximate the slope of the tangent line drawn to the graph of y = 2sinx + cosx at x = 4.2. Round your answer to 2 decimal places.

Answer 1

On your graphing calculator, press Y= and type in your function.  Make sure your calculator is in radians mode, otherwise the graph will not show properly when you construct it.  Then press GRAPH to see the graph.  Then, press 2ND, CALC, scroll down and select dy/dx.  Hit ENTER.  The calculator will ask you to enter an x value.  Enter 4.2, and press ENTER.  Your slope of the tangent line will be displayed for that point on the bottom of the screen.

 

You should get -0.11 as your slope of the tangent line.

Answer 2

 

To find slope, you have to find the derivative:

 

y = 2sinx + cosx

y' = 2cosx - sinx

 

To find slope at x = 4.2, plug that value into the derivative & make sure your calculator is in radians:

 

y' = 2cos(4.2) - sin(4.2) = -0.11

Answer 3

y = 2sinx + cosx

 

m = y'(x)

 

y'(x) = 2cosx - sinx

 

I assume the 4.2 is radians.  You should state in the problem whether the angle is in radians or degrees.

 

y'(4.2) = 2cos4.2 - sin4.2

 

You can finish from here.