onegirl
Find an equation of the tangent line to h(x) = f(x)g(x) at x = 1
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ingenuus
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\[y=[f'(1)g(1) + f(1)g'(1)](x-1) + f(1)g(1)\]
campbell_st
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well you need the point of the curve which will be (1, h(1))
you need to find the slope... but 1st you need to differentiate the function using the product rule
h'(x) = f(x)g'(x) + g(x)f'(x)
the slope at x = 1 is found by substituting x = 1 into the 1st derivative(above)
h'(1) = f(1)g'(1) + g(1)f'(1)
now you have a slope h'(1) and point (1, h(1))
use the point slope formula to find the equation of the tangent.
onegirl
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ok
onegirl
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so i got y = g(1)f'(1) + f(1)x g'(1) - f(1) g'(1) + f(1)g(1) is it correct?
onegirl
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@campell_st ?
onegirl
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@campbell_st
onegirl
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@ingenuus did i get it right?
ingenuus
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no the answer is above
onegirl
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okay
ingenuus
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do you understand the equation y=m(x-a) +b ?
onegirl
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yes
ingenuus
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what is the slope m in your case
onegirl
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1?
ingenuus
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why is it 1?