Question

Sketch the graph of a continuous function on (-4,0 satisfying the given properties f')0 for x = -3 and - 2. f has an absolute maximum x 0;fhas an absolute minimum at Choose the correct graph below and has a local minimum at x-2

Answer 1

Option A is correct.

f:[-4,0] → IR f'(x)=0 for 23-3, and x = -2 At x= o f has absolufe maximum At --4 :f has absolute minimum At I--2.f has local minimum. 6 ... ... Here and I am explaining why option (A) is correct other options are wrong. from Gruph. Funchin is differentiable at X=-3 4-2 and property is sahished. also property 0,0 and are satisfied. At - f has local minima 4 At-3 f has local maxima. f'(-3)20 f(-4)= 0 = f(x) f(0) = 30 = property « 3 satisfied. Here f is not differentiable at aa-3 & 1 = -2 .: property is violeted. Couph has sharp corner. at a=-3 & 1=2

ON In option . Also thas sharp corner at 22 X=-3 & X=-2 : Function is not differentiable at these points. La property is not satisfied . A 2 # In option D property & are violeted because f has absolute maximum at x=-. instead of absolute minimum. & also f has absolute minimum at xao - instead of absolute maximum. -4 -8 -2 ox I Graph of f