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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 =
 one year ago
 one year ago
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 =
 one year ago
 one year ago

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campbell_stBest ResponseYou've already chosen the best response.1
can you find the derivative of the curve...?
 one year ago

campbell_stBest ResponseYou've already chosen the best response.1
ok... have you done or are you doing calculus?
 one year ago

campbell_stBest ResponseYou've already chosen the best response.1
ok... can you differentiate y = x^4...?
 one year ago

campbell_stBest ResponseYou've already chosen the best response.1
and can you differentiate \[ y = 4e^{x} \]
 one year ago

campbell_stBest 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 \[y = 4e^x\]
 one year ago

campbell_stBest 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)
 one year ago

campbell_stBest 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..?
 one year ago

campbell_stBest 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...?
 one year ago

campbell_stBest ResponseYou've already chosen the best response.1
can you try again..
 one year ago

campbell_stBest 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..?
 one year ago

campbell_stBest ResponseYou've already chosen the best response.1
that looks good... so there you have your solutions.
 one year ago

campbell_stBest ResponseYou've already chosen the best response.1
hope it helps... you do need to practice you differentiation basics.
 one year ago
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