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Ex 6.5,1 - Chapter 6 Class 12 Application of Derivatives - Part 22

Ex 6.5,1 - Chapter 6 Class 12 Application of Derivatives - Part 23
Ex 6.5,1 - Chapter 6 Class 12 Application of Derivatives - Part 24
Ex 6.5,1 - Chapter 6 Class 12 Application of Derivatives - Part 25

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Ex 6.5,1 (Method 1) Find the maximum and minimum values, if any, of the following functions given by (iv) f(π‘₯) = π‘₯3 + 1f(π‘₯)=π‘₯^3+1 Finding f’(x) f’(π‘₯)=𝑑(π‘₯^3 + 1)/𝑑π‘₯ =3π‘₯^2 Putting f’(𝒙)=𝟎 3π‘₯^2=0 π‘₯^2=0 π‘₯=0 Therefore by first derivate test, the point π‘₯=0 is neither a point of local maxima nor a point of local Minima Hence 𝒙=𝟎 is point of inflexion Hence, there is no minimum or maximum value Ex 6.5, 1 (Method 2) Find the maximum and minimum values, if any, of the following functions given by (iv) f(π‘₯) = π‘₯3 + 1 π‘₯=0 Finding f’’(x) f’(x) = 3x2 f’’(x) = 6x Finding f’’(x) at x = 0 f’’(0) = 6 Γ— 0 = 0 Since f’’(x) = 0 at x = 0 ∴ The point π‘₯=0 is neither a point of local maxima nor a point of local Minima Hence 𝒙=𝟎 is point of inflexion Hence, there is no minimum or maximum value

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