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Show that the function given by f(x) = 7...

Show that the function given by `f(x) = 7x-3`is strictly increasing on R.

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To show that the function \( f(x) = 7x - 3 \) is strictly increasing on \( \mathbb{R} \), we will follow these steps: ### Step 1: Find the derivative of the function The first step is to differentiate the function \( f(x) \). \[ f(x) = 7x - 3 \] ...
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NCERT ENGLISH-APPLICATION OF DERIVATIVES-SOLVED EXAMPLES
  1. Show that the function f(x) = cos x (i) is strictly decreasing funct...

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  2. Prove that the function f given by f(x)=x^3-3x^2+4x is strictly increa...

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  3. Show that the function given by f(x) = 7x-3is strictly increasing on ...

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  7. A stone is dropped into a quiet lake and waves move in a circle at ...

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  8. The volume of a cube is increasing at the rate of 9 cm^3/sec. How fa...

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  9. Find the rate of change of the area of a circle with respect to its ...

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  10. Find the equation of the tangent to the curve y=(x-7)/((x-2)(x-3) at ...

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  11. Find the equations of the tangent and the normal to the curve x^(2/...

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  12. Find the intervals in which the function f given by f(x)=x^2-4x+6is (a...

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  13. Find the intervals in which the function f given by f(x)=4x^3-6x^2-72 ...

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  14. ) Find the intervals in which the function sin 3x, x in [0, pi/2], is ...

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  15. Find the intervals in which the function f given f(x)=\ s in x+cosx ,\...

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  16. Find the slope of the tangent to the curve y = x^3- x at x = 2.

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  17. Show that the altitude of the right circular cone of maximum volume th...

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  18. Find the equation of all lines having slope 2 and being tangent to th...

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  19. Find the points on the curve (x^2)/4+(y^2)/(25)=1 at which the tang...

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  20. A circular disc of radius 3 cm is being heated. Due to expansion, i...

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