Graphing from the derivative
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Please sketch a graph of a function f have the indicated characteristics. Please explain.
(a) f(0) = f(2) = 0
f'(x) > 0 if x <1
f'(1) = 0
f'(x) < 0 if x > 1
f''(x) < 0
(b) f(0) = f(2) = 0
f'(x) < 0 if x < 1
f'(1) = 0
f'(x) > 0 if x > 1
f''(x) > 0
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Solution Summary
This shows how to sketch graphs with the given characteristics of the derivative.
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Differentiation
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Please sketch a graph of a function f have the indicated characteristics. Please explain.
(a) f(0) = f(2) = 0 f'(x) > 0 if x <1 f'(1) = 0
f'(x) < 0 if x > 1 f''(x) < 0
Solution :
f(0) = f(2) = 0 » The graph cuts the x-axis at those x-values. Hence our
graph passes through the x-axis at x = 0 and x = 2
f'(x) > 0 if x < 1 » First derivative means slope ... slope is positive , when our
graph at that region , ...
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