1. Let f(x)={x^2, x is less than or equal to 1 {2x, x> 1 a. Use the alternate fo
ID: 3193698 • Letter: 1
Question
1. Let f(x)={x^2, x is less than or equal to 1
{2x, x> 1
a. Use the alternate form definition to find the left-hand derivative of f at x =1 if it exists.
b. Use the alternate form definition to find the right-hand derivative of f at x =1 if it exists.
c. Is f(x)differentiable at x =1? Explain.
d. Determine if f(x) is continuous at x =1. Give conclusion based on the 3-step definition.
e. Sketch a graph of f(x) . Be sure to label it.
f. On the same set of axes, sketch a graph of f'(x). Use a different line quality, and be sure to label it.
Explanation / Answer
a) 2x b) 2 c) Yes because the left and right hand limits of the derivatives equal 2 as x approaches 1. d) Yes because the limit as x approaches 1 is the same as f(1).
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