Most Important Selected Qs for JEE AdvancedMathematicsContinuity and Differentiability
Let f(x)= array lr ⁻¹ x, & -1 x < 0 ⁻¹ x, & 1 x 0 array . and g(x)= array ll ⁻¹ x, & -1 x < 0 ⁻¹ x, & 1 x 0 array . . If h(x)= . f(x), g(x) , then:
Options
- Ah(x) is continuous x [-1,1]
- Bh(x) is non derivable at exactly one point in x (-1,1)
- Cminimum value of h(x) is equal to - 4
- Dmaximum value of h(x) is equal to 4
Correct answer
D. maximum value of h(x) is equal to 4
Step-by-step solution
f(x)= array lc ⁻¹ x, & -1 x < 0 ⁻¹ x, & 0 x 1 array . and g(x)= cases ⁻¹ x, & -1 x < 0 ⁻¹ x, & 1 x 0 cases h(x)= f(x), g(x) = [ array ll g(x), & -1 x < 0 f(x), & 0 x < 1 2 g(x), & 1 2 x 1 array .h(x)= [ array ll ⁻¹ x, & -1 x < 0 ⁻¹ x, & 0 x < 1 2 ⁻¹ x, & 1 2 x 1 array . h(x) is continuous and not differentiable at x=-1, 1 2 , 1 and h_ =h ( 1 2 )= 4