Find the stationery points of x^3 + 3x^2 - 24x + 7 and determine whether the slope is increasing or decreasing at x=3.
i) We must differentiate the equation and set it equal to 0 to find stationery points:
dy/dx = 3x2 + 6x + 24=0 Note we can take out a factor of 3 x2+ 2x - 8=0 Factorise (x-2)(x+4)=0 State x values x=2 or -4
Now we have the x values of the stationery points of the curve, so we substitute into the original equation for the y values to getS.P=(2, -21) and (-4, 87).To find whether the curve is increasing or decreasing at x=3 substitute into the derivative and evaluate. If positive then its increasing and if negatuve then its decreasing, in this case it is negative so the curve is decreasing at x=3.
