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 2 years ago
The twicedifferentiable function f is defined for all real numbers and satisfies the
following conditions: f(0) = −2 ,
f′(0) = 3, f"(0) = −1 .
A. The function g is given by g(x) = tan(ax) + f(x) for all real numbers, where a is a
constant. Find g′(0) and g"(0) in terms of a.
 2 years ago
The twicedifferentiable function f is defined for all real numbers and satisfies the following conditions: f(0) = −2 , f′(0) = 3, f"(0) = −1 . A. The function g is given by g(x) = tan(ax) + f(x) for all real numbers, where a is a constant. Find g′(0) and g"(0) in terms of a.

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Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1just differentiate and let x=0. \(g'(0) = a sec^2 (0) +f'(0)\) where \(sec^2(0)=1\), so, \(g'(0) = a +3\)

isai
 2 years ago
Best ResponseYou've already chosen the best response.0Can you help me with the second part too? The function h is given by ℎ(x) = sin(kx) ∙ f(x) for all real numbers, where k is a constant. Find ℎ′(x) and write an equation for the line tangent to the graph of h at x=0. please?

Shadowys
 2 years ago
Best ResponseYou've already chosen the best response.1sure...for this question, you too find the h'(0) to get the gradient at that pt, but this time you also have to evaluate h(0) to get the point(0,h(0)) \(h'(0)=k \cos (0) f(0) + f'(0) sin(0)\) \(h'(0)=2k\)

isai
 2 years ago
Best ResponseYou've already chosen the best response.0Thank you sooo much! I highly appreciate it :)
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