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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.
 one year ago
 one year 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.
 one year ago
 one year ago

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

isaiBest ResponseYou've already chosen the best response.0
Can 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?
 one year ago

ShadowysBest ResponseYou've already chosen the best response.1
sure...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)) \(h'(0)=k \cos (0) f(0) + f'(0) sin(0)\) \(h'(0)=2k\)
 one year ago

isaiBest ResponseYou've already chosen the best response.0
Thank you sooo much! I highly appreciate it :)
 one year ago
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