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If f(x) = e^x, what is the value of f''(0)? (2021)
If f(x) = e^x, what is the value of f''(0)? (2021)
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If f(x) = e^x, what is the value of f''(0)? (2021)
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f'(x) = e^x and f''(x) = e^x. Therefore, f''(0) = e^0 = 1.
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Q: If f(x) = e^x, what is the value of f''(0)? (2021)
Solution:
f'(x) = e^x and f''(x) = e^x. Therefore, f''(0) = e^0 = 1.
Steps: 6
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Step 1: Identify the function given in the question, which is f(x) = e^x.
Step 2: Find the first derivative of the function, f'(x). The derivative of e^x is e^x, so f'(x) = e^x.
Step 3: Find the second derivative of the function, f''(x). The derivative of f'(x) = e^x is also e^x, so f''(x) = e^x.
Step 4: Evaluate the second derivative at x = 0. Substitute 0 into f''(x): f''(0) = e^0.
Step 5: Calculate e^0. The value of e^0 is 1.
Step 6: Conclude that f''(0) = 1.
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