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Let `f: Rvec` be a differentiable function `AAx in R` . If the tangent drawn to the curve at any point `x in (a , b)` always lies below the curve, then `f^(prime)(x)<0,f^(x)<0AAx in (a , b)` `f^(prime)(x)>0,f^(x)>0AAx in (a , b)` `f^(prime)(x)>0,f^(x)>0AAx in (a , b)` `non eoft h e s e`

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The correct Answer is:
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Clearly for`f(x) gt0 f''(x) gt0` [in figure (c ) tangent always lies below the graph
For `f'(x) lt0, f''(x) lt["in figure" (d)]` tangent always lies below the graph.
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CENGAGE ENGLISH-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise
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  2. Let f: RvecR be a differentiable function for all values of x and has ...

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  3. Let f: Rvec be a differentiable function AAx in R . If the tangent dr...

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  4. Let f(x) be a function such that f^(prime)(x)=(log)(1/3)[(log)3(sinx+a...

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  9. Suppose that f is a polynomial of degree 3 and that f^(x)!=0 at any of...

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  11. If varphi(x) is a polynomial function and varphi^(prime)(x)>varphi(x)A...

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  12. If f''(x) gt forall in R, f(3)=0 and g(x) =f(tan^(2)x-2tanx+4y)0ltxlt(...

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  13. If f(x)=x+sinx ,g(x)=e^(-x),u=sqrt(c+1)-sqrt(c) v=sqrt(c) -sqrt(c-1),(...

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  19. If f(x)=alog|x|+b x^2+x has extreme values at x=-1 a n d a t x=2, then...

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  20. If a function f(x) has f^(prime)(a)=0a n df^(a)=0, then (a) x=a is a...

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