@coolnero Thanks! :)
For Q8 we don't need to go for differentiation and all
f(x) = ax^2 – b|x|
x^2 and |x| are always non negative.
If a > 0 and b < 0, f(x) > = 0
So at x = 0, f(x) is minimum when a > 0 and b < 0
A quadratic function f (x ) = ax^2 + bx + c, can be expressed in the standard form : a(x-h)^2 + k by completing the square. The graph of f(x) is a parabola with vertex (h,k); the parabola opens upward if a > 0 or downward if a < 0.
Maximum or Minimum Value of a Quadratic Function
Let f be a quadratic function with standard form f (x) = a( x − h )^2 + k. The maximum or minimum value of f occurs at x = h If a > 0, then the minimum value of f is f(h) = k. If a < 0, then the maximum value of is f (h) = k
We now derive a formula for the maximum or minimum of the quadratic function F(x) = ax^2 + bx + c. For either of the two cases (the quadratic having a maxima or a minima), the maxima or the minima, as the case may be, will occur when x = - b/2a the maximum or minimum value is f(-b/2a) = c - b^2/4a remember that - b/2a = sum of roots/2
Thanks for replying Sir.You completely cleared my confusion! please help me with this also: In last category of questions: no.1 (8/x)+(7/y)=1/3 total solutions are given to be 2T-1 =47 and positive solutions are T-1=23 so what are remaining soltions (47-23)?? if negative solutions are mentioned to be 0??
@anurag_chauhan The last sum is some sort of miscalculation I guess, because according to the sum when y = 1 then x = 1 * 6 and not vice versa. In that case the value of y extends upto 100 and x upto 496 * 501 for which the ans should be 501.