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v.s
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Find equations of the tangent line and normal line to the curve at the given point.
y = x^4 + 4e^x, (0, 4)
tangent line y =
normal line y =
 2 years ago
 2 years ago
v.s Group Title
Find equations of the tangent line and normal line to the curve at the given point. y = x^4 + 4e^x, (0, 4) tangent line y = normal line y =
 2 years ago
 2 years ago

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campbell_st Group TitleBest ResponseYou've already chosen the best response.1
can you find the derivative of the curve...?
 2 years ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
ok... have you done or are you doing calculus?
 2 years ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
ok... can you differentiate y = x^4...?
 2 years ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
and can you differentiate \[ y = 4e^{x} \]
 2 years ago

v.s Group TitleBest ResponseYou've already chosen the best response.0
or is it x4e^x
 2 years ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
quick lesson \[y = 4e^{f(x)} ..... then .... y'=4f'(x) e^{f(x)}\] and in your question f(x) = x... try the derivative again for \[y = 4e^x\]
 2 years ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
not quite if f(x) = x f'(x) = 1 so its y' = 4e^x so you you function the derivative is \[y' = 4x^3 + 4e^x\] ok... you now have the equation for the slop of the tangent...(1st derivative) subsitiute x = 0 to find the slope of the tangent at the point (0, 4)
 2 years ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
thats correct so you have a tangent or line with a slope of 4 and point (0, 4) can you find the equation of the line...? for the normal... the slope will be the negative reciprocal of the slope of the tangent... what would the slope of the normal be..?
 2 years ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
no... ok... lets step back... you have a slope of 4 and point (0, 4) the equation of the tangent will be y = 4x + b or using the formula \[y  4 = 4(x  0)\] whats the equation of the tangent...?
 2 years ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
can you try again..
 2 years ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
ok... thats the equation of the tangent... now the normal... which is perpendicular to the tangent... the slope is the negative reciprocal of the tangent... so if the tangent has a slope of 4 ... what is the slope of the normal..?
 2 years ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
that looks good... so there you have your solutions.
 2 years ago

campbell_st Group TitleBest ResponseYou've already chosen the best response.1
hope it helps... you do need to practice you differentiation basics.
 2 years ago
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