Question

(5 points) The function f(x) = 5x + 7x-1 has one local minimum and one local maximum. This function has a local maximum at x = with value and a local minimum at x = with value

Answer 1

solution:- given function floo=50+78' St derivative; f'(x)=5(1)+7(-1)&² [flaxy = 5-7 - for minima or maxima f'(X) =0 1 1 1 1 1 1 1

® Now again differentiate equation f(x)= 0-2 (-2)* f"GX) = 1423 f"«x) = het 3

2fh=5x + 2 aty=-SE), f"-sg1 = elemente n a negative a praxing & max. value of function at x = -A f(-5) = 5(-1) + e = -5*JE - 7x =-55x57 - 57455 = -535 – 535 f(-572) =-2535 | max.value Not at x=+57) , f (575) = 1 1 1 1 = Positive of minima & min. value of function at a=573 1. f( 57 ) = 5(52) + 7 = 5x5A + 7x E = 5 x 57 x 57 x5 = 535 x 335 f(1/2) =2835 min. value.

Hence the function - has maximam at x=/-) with value 52 535] s my & a local minimum at x= with value [2.35 J