anonymous
  • anonymous
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 =
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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campbell_st
  • campbell_st
can you find the derivative of the curve...?
anonymous
  • anonymous
i don't know
campbell_st
  • campbell_st
ok... have you done or are you doing calculus?

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anonymous
  • anonymous
doing calculus
campbell_st
  • campbell_st
ok... can you differentiate y = x^4...?
anonymous
  • anonymous
4x^3
campbell_st
  • campbell_st
and can you differentiate \[ y = 4e^{x} \]
anonymous
  • anonymous
x4e
anonymous
  • anonymous
or is it x4e^-x
campbell_st
  • campbell_st
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 \[y = 4e^x\]
anonymous
  • anonymous
4xe^-x
campbell_st
  • campbell_st
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)
anonymous
  • anonymous
y'=4
campbell_st
  • campbell_st
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..?
anonymous
  • anonymous
=-1/4x^3+4e^x
campbell_st
  • campbell_st
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...?
anonymous
  • anonymous
y=4x-4
campbell_st
  • campbell_st
can you try again..
anonymous
  • anonymous
y=4x+4
campbell_st
  • campbell_st
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..?
anonymous
  • anonymous
y=-1/4x+4
campbell_st
  • campbell_st
that looks good... so there you have your solutions.
anonymous
  • anonymous
thank you
campbell_st
  • campbell_st
hope it helps... you do need to practice you differentiation basics.
anonymous
  • anonymous
yeaa

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