First slide
Mean value theorems
Question

 Let f(x) be any function continuous and twice differentiable function on (a,b) . If for 

 all x(a,b),f'(x)>0 and f''(x)<0, then for any c(a,b),f(c)-f(a)f(b)-f(c) is greater  than 

Difficult
Solution

 Since f'(x)>0, the function f is increasing and since f"(x)<0, the function downward facing

Nm So, slope of AC will be greater than slope of BC i.e., f(c)-f(a)c-a>f(b)-f(c)b-cf(c)-f(a)f(b)-f(c)>c-ab-c

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