- #1

chwala

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- Homework Statement
- Kindly see attached

- Relevant Equations
- differentiation

Part (a) no problem...chain rule

##\dfrac{dy}{dx}= (2x+3)⋅ e^{x^2+3} =0##

##x=-1.5##

For part b,

We need to determine and check if ##\dfrac{d^2y}{dx^2}>0##

...

##\dfrac{d^2y}{dx^2}=e^{x^2+3x} [(2x+3)^2+2)]##

Now any value of ## x## will always give us, ##\dfrac{d^2y}{dx^2}>0##

The other way/approach would be to pick any two points on the curve and check whether the straight line joining the two points lies under/over the curve to ascertain convex property.