Question

1. (15 points - 3 each) True or false? Justify your answers. (a) The value of a function near x = a can be well approximated using the tangent line at a (if the function is differentiable at a). (b) The only way for a value x = b to be a critical point is if f'(6) = 0 (c) It is possible for a graph to be both increasing and concave up at the same time. (d) If F(x) + 9) = f(x), then F(x) is an antiderivative of f(x). (e) When optimizing, you can only find the maximum value of a function, not the minimum

Answer 1

Solution (1) (a) The value of function near na can be well Lpproximated True using the tongent line at a... Because at point where tongeost touces the curre will give approximate value of function. (b) The only way for a value x=b to be acoistical polot s5 F F"(b)=0. False Justifications Smee Critical point is all the point where fluo or fia) is not defined. increasing (C) It is possiblee foro graph to be both increasi False. and con care cup at the same point Justiffcation : At point where function is com care up is forinto of minimum hence graph changes from dec decresing to no increasing at that point 100) If on [F(x) +9] = Flag , then fixo é coll derivative of fall True.