DerivativeApplications

# Problems with conditions

Example 1: Calculate the value of *a* and *b* to make the function:

f(x) = ax^{3} + bx

have a relative minimum in (1,2)

Example 2: (PAEG - Reserve 2 - 2008) Determine the value of

*a,b*€**R**, so that the function: f(x) =*asinx + bcosx*passes through point (π/4,√2) and the slope of the tangent line at the point of abscissa x =π/2 is 5. Calculate the derivative of order 2008 of this function.**Exercise**: Determine

*a,b,c*to make the function f(x) = x

^{3}+ ax

^{2}+ bx + c have a maximum in x=−4, a minimum in x=0 and it passes through the point (1,1).

Solution:

*a*= 6,*b*= 0,*c*= -6Licensed under the Creative Commons Attribution Non-commercial Share Alike 3.0 License