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clara1223
 one year ago
given g(2)=3, g'(2)=2, h(2)=1, h'(2)=4
a) if f(x)=2g(x)+h(x), find f'(2)
b) if f(x)=4h(x), find f'(2)
c) if f(x)=g(x)/h(x), find f'(2)
d) if f(x)=g(x)h(x), find f'(2)
clara1223
 one year ago
given g(2)=3, g'(2)=2, h(2)=1, h'(2)=4 a) if f(x)=2g(x)+h(x), find f'(2) b) if f(x)=4h(x), find f'(2) c) if f(x)=g(x)/h(x), find f'(2) d) if f(x)=g(x)h(x), find f'(2)

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.0for each, first find \(f'(x)\), then plugin \(x=2\)

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0I am still confused, can you walk me through a and I'll see if I can do the rest on my own?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm f(x)=2g(x)+h(x)\]The derivative of f(x), with respect to x, is f'(x), yes?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1Likewise, the derivative of g(x), with respect to x, is g'(x). There is nothing fancy going on in this first problem. No product rule, no composition, nothing special :)\[\large\rm f'(x)=2g'(x)+h'(x)\]

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0oh, and then you would plug in the given values of g'(x) and h'(x)?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm f'(\color{orangered}{x})=2g'(\color{orangered}{x})+h'(\color{orangered}{x})\]They want us to evaluate this at x=2,\[\large\rm f'(\color{orangered}{2})=2g'(\color{orangered}{2})+h'(\color{orangered}{2})\]And yes, use that chart at the top to plug in the missing pieces on the right :)

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0great! so it would be 2(2)+4, so 0
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