Home › JEE Main › Mathematics › Application of Derivatives › Function f is INCREASING on interval (a, b) if:
Function f is INCREASING on interval (a, b) if:
Af = 0
Bf' = 0
Cf'(x) > 0 for all x in (a, b)
Df'' < 0
Answer & Solution
Correct answer: C. f'(x) > 0 for all x in (a, b)
If f'(x) > 0 on an interval, f is increasing there. Similarly, f'(x) < 0 implies decreasing. (Strict inequality gives strict monotonicity.)
Related questions
Elasticity of demand is given byProfit is maximised whereMarginal revenue (MR) for a price-taking firm (perfect competition) equalsMarginal cost (MC) isTwo numbers have a sum of $24$. Their product is largest when the numbers areFor $f(x)=3x^4-8x^3+12x^2-48x+25$ on $[0,3]$, the critical point inside the interval isA cylindrical tank of radius $10$ m is filled with wheat at $314$ m$^3$/h. The depth of thThe maximum value of $[x(x-1)+1]^{1/3}$ for $0\le x\le 1$ is