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How do you find the slope of the graph #g(t)=2+3cost# at (pi,-1)?

Answer 1

Emma Aldridge

See explanation.

To find a slope of a graph at a specified point you have to calculate the value of first derivative at this point.

If #g(t)=2+3cost# then:

#g'(t)=3*(-sint)=-3sint#

Now at the point #x_0=pi# the derivative is:

#g'(pi)=-3sinpi=-3*0=0#

The slope of the graph at #(pi,-1)# is #0#.

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Answer 2

Evelyn Agard

To find the slope of the graph of ( g(t) = 2 + 3\cos(t) ) at ( t = \pi ), we need to find the derivative of ( g(t) ) with respect to ( t ) and evaluate it at ( t = \pi ).

The derivative of ( g(t) ) with respect to ( t ) is ( g'(t) = -3\sin(t) ).

Evaluating ( g'(t) ) at ( t = \pi ), we get ( g'(\pi) = -3\sin(\pi) = 0 ).

So, the slope of the graph of ( g(t) ) at ( t = \pi ) is ( 0 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.