Find the value of a that makes the following function differentiable for all values of x. ax if x<0 g(x) = x2 - 7x if x20 The function g(x) is differentiable for all values of x when a = (Simplify your answer.)

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A: Given -  To find - Find

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A: It is known that every exponential function is continuous on the interval -∞,∞.

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A: using the concept of composition function.

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Q: Let h(x)=f(x)g(x). If f(x)=4x^2−4x+4,g(−1)=2, and g′(−1)=0, what is h′(−1)? Do not include…

A: Given, h(x)=f(x)g(x), f(x)=4x2−4x+4, g(−1)=2  and g′(−1)=0 f(-1) = 4-4+4 = 4 f'(x) = 8x-4 ∴ f'(-1)=…

Q: B. Evaluate the piecewise function below at the given values of x. if -1 1 1.f(-1) 2. f(5) 3. (e)

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Q: (2x² + 5, if x 5 Consider the function h(x) = Find the value of B such that h(x) is continuous at x…

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Q: (1) The function f(x) is such that f(x)= 4x' +21x² +36x- 20 Ca) Find f '(x) & f"(x)

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Q: See attached

A: The given function:

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Q: The function g (æ) = |x² – 4| is differentiable at x = 4 . - True False

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Q: Find a value of the constant k, if possible, that will make the function continous everywhere if…

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Q: Let h(x) = f(x)g(x). If f(x) = –3x² + 2x – 3 and g(x) = –3x² + 4x + 3, what is h' (1)? Do not…

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