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Write True/False: If f(x) has an absolu...

Write True/False:
If f(x) has an absolute maximum at x=c, then f'( c )=0

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To determine whether the statement "If f(x) has an absolute maximum at x=c, then f'(c)=0" is true or false, we can analyze the concept of absolute maxima in calculus. ### Step-by-Step Solution: 1. **Understanding Absolute Maximum**: - An absolute maximum at a point \( x = c \) means that the value of the function \( f(c) \) is greater than or equal to the values of the function at all other points in its domain. In mathematical terms, \( f(c) \geq f(x) \) for all \( x \) in the domain of \( f \). 2. **Role of the Derivative**: ...
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MAHAVEER PUBLICATION-DIFFERENTIATION OR DERIVATIVE OF A FUNCTION-QUESTION BANK
  1. Write True/False: If f'( c ) does not exist and f'(x) changes from po...

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  2. Write True/False: If f'( c ) exists and f'( c )gt0, then f(x) has a l...

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  3. Write True/False: If f(x) has an absolute maximum at x=c, then f'( c ...

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  4. Write True/False: If f'( c )=0 then f(x) has a local maximum or a loc...

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  5. Let y=f(x) and z=g(x) be two curves. Then the tangents drawn to curves...

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  6. Given, f(x)=x^3-5x+2. Then f'(2) equals

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  7. d/dx(sinx^2)=?

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  8. Differentiate ax^2+b

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  9. d/dx[(x+1)^3/x]=?

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  10. The derivative of y=|x-2| at x=2 is

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  11. Given the polar equation r=1. find dy/dx.

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  12. The slope of the normal to the curve y=2x^(2)+3sin x at x=0 is :

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  13. The line y=x+1 is a tangent to the curve y^(2)=4x at the point:

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  14. The slope of the tangent line to the curve y=x^3-2x+1 at x=1 is

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  15. Find the slope of the line whose parametric equations are x=4t+6 and y...

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  16. The slope of the tangent line to the curve x+y=xy at the point (2,2) i...

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  17. Find the coordinates of the vertex of the parabola y=x^2-4x+1 by makin...

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  18. Find the point in the parabola y^2=4x at which the rate of change of t...

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  19. Find the eqaution of the normal to x^2+y^2=5 at the point (2,1)

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  20. Find the point on the curve y=3x^2-4x+5 where the tangent line is para...

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