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Find the minimum value of the function, f(x) = x*exp(x)

The minimum value lies where the tangent to the curve has a gradient of zero and the curve approaching from both directions increases in value. This is done by finding the first and second derivatives of the...
RT
Answered by Robin T. • Maths tutor
4184 Views

Differentiate y=e^(x)*sin(x) with respect to x

y=e^(x)*sin(x) Use the product rule: y'=uv'+vu' y=u*v Differentiate: u=e^(x) u'=e^(x) v=sin(x) v'=cos(x) Sub into the product rule: y'=e^(x)*cos(x)+e^(x)*sin(x) Take out a factor of e^(x): y'=e^(x)*(cos(x)+s...
AJ
Answered by Alexander J. • Maths tutor
6261 Views

Find dy/dx in terms of t of the parametric equations x=4e^-2t, y=4 - 2e^2t

x=4e -2t , y=4-2e 2t dy/dx = dy/dt * dt/dx dy/dt = -4e 2t dx/dt = -8e -2t dt/dx = -1/8 * e 2t dy/dx = (-4e 2t )(-1/8 * e 2t ) = 1/2 * e 4t dy/dx = 0.5e 4t
JM
Answered by Josh M. • Maths tutor
6169 Views

Core 1 question: Draw the graph "y = 12 - x - x^2"

I always found drawing graphs one of the hardest parts of maths - especially in C1 where you cannot use a calculator to help you. So, I used some simple rules to find key parts of the graph which would simpl...
TH
Answered by Tess H. • Maths tutor
8677 Views

Solve x^2 > |5x - 6|

We need to split the problem into two cases to remove the abs sign. Case 1: 5x - 6 >= 0, equivalent to x >= 6/5. In this case the problem is now to find the values of x that satisfy x 2 > 5x - 6. Re...
JH
Answered by James H. • Maths tutor
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