(T/F) The derivative f\'(a) is the instantaneous rate of change of y = f(x) with
ID: 2882605 • Letter: #
Question
(T/F) The derivative f'(a) is the instantaneous rate of change of y = f(x) with respect to x when x = a. (T/F) If'(x) > 0 on an interval, then f is increasing on that interval. (T/F) If y = e^2, then y' = 2e (T/F) If f and g are differentiable, then d/dx [f(x) + 2g(x) = d/dx (f(x)) + 2 d/dx(g(x)) (T/F) If f and g are differentiable, then d/dx [f(x) middot g(x)] = d/dx(f(x)) middot d/dx (g(x)) (T/F) If f and g are differentiable, then d/dx[f(g(x))] = f'(g'(x)) = f'(g'(x)) + g'(x) (T/F) If f is continuous at a, then f is differentiable at a. (T/F) d^2 y/dx^2 = (dy/dx)^2 (T/F) d/dx(ln 10) =1/10Explanation / Answer
From the given question,
1. T derivative f'(a) is instatntaneous rate of change of f(x) at a.
2.T if f'(x) >0, slope is positive, so function is increasing.
3.F if y=e2, y'=0 as e2 is a constant.
4.T if y=f+2g then dy/dx= df/dx + 2 dg/dx
5. F if y=f.g then dy/dx=f dg/dx + g df/dx
6.F if y=f(g(x)) the y' = f'(g(x)) g'(x)
7.F not necessary. y=|x| is continous at 0, but not differentiable at 0.
8.F d2y/dx2= d/dx( dy/dx)
9.F d/dx(ln 10)= 0 as it isa constant.
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