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Find the slope of the tangent to the cur...

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

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To find the slope of the tangent to the curve \( y = x^3 - x \) at \( x = 2 \), we will follow these steps: ### Step 1: Differentiate the function We start with the function: \[ y = x^3 - x \] To find the slope of the tangent, we need to compute the derivative \( \frac{dy}{dx} \). ...
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NCERT ENGLISH-APPLICATION OF DERIVATIVES-SOLVED EXAMPLES
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  2. Find the intervals in which the function f given by f(x)=4x^3-6x^2-72 ...

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

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

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

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

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

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

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

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  10. Show that the function f given by f(x)=tan^(-1)(sinx+cosx), x" ">" "0 ...

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  11. A water tank has the shape of an inverted right circular cone with it...

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  12. A car starts from a point at time second and stops at point ....

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  13. An Apache helicopter of enemy is flying along the curve given by y=x^...

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  14. Find absolute maximum and minimum values of a function f given by f...

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  15. Find intervals in which the function given by f(x)=3/(10)x^4-4/5x^3-3x...

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  16. Find the equation of tangents to the curve y=cos(x+y),-2pilt=xlt=2pi t...

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  17. Find the equation of the normal to the curve x^2=4\ y which passes ...

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  18. A man 2 metres high walks at a uniform speed of 5 km/hr away from a ...

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  19. An open topped box is to be constructed by removing equal squares fro...

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  20. A manufacturer can sell x items at a price of Rs. (5-x/(100)) each. Th...

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