The function p is defined for all real numbers by
p(x)={sinx,excosx,x≤0,x>0.
Numerical work should be shown to at least three decimal places.
(a) Approximate p′(0−) and p′(0+), the left-hand and right-hand derivatives of p at x=0. Present the numerical values and describe your computational approach.
(b) Using the results from part (a), determine whether p is differentiable at x=0. Justify your conclusion by referencing the formal definition of differentiability.
(c) Compute an accurate numerical approximation for p′(1). Then write the equation of the line tangent to the graph of p at x=1.