Which interval/s is the function decreasing and is concave up? What are the critical numbers ? And does the function have a max/minimum? Suppose the derivative of a function is x2 + 2x - 3.a) On which open interval/s is the function decreasing?b) On which open interval/s is the function concave up?c) What is/are the critical number/s of the function? In other words, for which x-value/s is the derivative zero? At these criticalnumbers, does the function have a maximum or minimum?Type your answer below.HTML EditorB IUA A I E E 3 E E x x, = E田,回¶ T 12ptParagraphO wordsGO

Consider the given: Given:f'x=x2+2x-3 Find the critical numbers: Substitute f'x=0x2+2x-3=0x2+3x-x-3=0xx+3-1x+3=0x+3x-1=0x=-3,1 Interval are -∞,-3,-3,1and1,∞a) On which intervals function is decreasing. The function is decreasing on the interval if f'x<0 in that interval.In Interval −∞,−3,f'−4=−42+2−4−3f'−4=16−8−3f'−4=5>0 IncreasingIn Interval −3,1,f'0=02+20−3f'0=0−3f'0=−3<0 decreasingIn Interval 1,∞,f'2=22+22−3f'2=4+4−3f'2=5>0 Increasing Hence, the function is decreasing in the open interval −3,1b) On which intervals is the function concave up? Find inflection points: f'x=x2+2x−3f''x=2x+2Substitute f''x=0,2x+2=0 x=−1Intervals are −∞,−1 and −1,∞ If f''x>0, then fx concave upwards.If f''x<0, then fx concave downwards.In Interval −∞,−1f''−2=2−2+2f''−2=−4+2f''−2=−2<0Concave downwardsIn Interval −1,∞f''0=20+2f''0=0+2f''0=2>0Concave upwards Hence, the function is concave up in the open interval −1,∞. c) The critical numbers of the function are -3 and 1. Yes, At critical numbers, the function have maximum or minimum. f''x=2x+2f''−3=2−3+2f''−3=−6+2f''−3=−4<0 Hence, the function has maximum at x=−3.f''1=21+2f''1=2+2f''1=4>0 Hence, the function has minimum at x=1.