- #1
mastermechanic
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<Moved from a technical section and thus a template variation>
1-) Question: Let f, g and h be differentiable everywhere functions with h(1) = 2 , h'(1) = - 3 , g(2) = -1 , g'(2) = 5 , f(-1) = 4 , f'(-1) = 7. Approximate the value of function F(x) = f(g(h(x))) at point x= 1.001
2-) My attempt: I think it's linear approximation question. I've generated the main functions by assuming their derivative as their slope.
If $$ h(1)=2 , h'(1) = -3 , (1,2) h(x) = -3x+5$$
If $$ g(2) = -1 , g'(2) = 5 , (2,-1) g(x) = 5x-11 $$
If $$ f(-1) = 4 , f'(-1) = 7 , (-1,4) f(x) = 7x+11$$
So $$ F(x) = f(g(h(x))) = [ 7[ 5 (-3x + 5) - 11 ] +11] $$
$$ F(x) = -105x + 109 $$
$$F(1.001) = 3.895 $$
Is it correct?
Thanks.
1-) Question: Let f, g and h be differentiable everywhere functions with h(1) = 2 , h'(1) = - 3 , g(2) = -1 , g'(2) = 5 , f(-1) = 4 , f'(-1) = 7. Approximate the value of function F(x) = f(g(h(x))) at point x= 1.001
2-) My attempt: I think it's linear approximation question. I've generated the main functions by assuming their derivative as their slope.
If $$ h(1)=2 , h'(1) = -3 , (1,2) h(x) = -3x+5$$
If $$ g(2) = -1 , g'(2) = 5 , (2,-1) g(x) = 5x-11 $$
If $$ f(-1) = 4 , f'(-1) = 7 , (-1,4) f(x) = 7x+11$$
So $$ F(x) = f(g(h(x))) = [ 7[ 5 (-3x + 5) - 11 ] +11] $$
$$ F(x) = -105x + 109 $$
$$F(1.001) = 3.895 $$
Is it correct?
Thanks.
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