Lagrange's Mean Value Theorem

JEE Main Mathematics · Applications of Derivatives · 8 questions, latest first

• Let f: R → R be a differentiable function such that f(0)=2. If |(d f)/(d x)| ≤ 3, for all x ∈ R, then f(1) lies in the interval20213 August, Shift 2 · Q70
• If the tangent to the curve, y=f (x)=x log_e x,(x>0) at a point (c,.f(c)) is parallel to the line - segment joining the points…20206 September, Shift 2 · Q59
• The position of a moving car at time t is given by f(t)=at^2+bt+c, t>0, where a, b and c are real numbers greater than 1. Then…20206 September, Shift 1 · Q60
• Let f be a twice differentiable function on (1,6). If f(2)=8, f^′(2)=5, f^′(x) ≥ 1 and f^′ ′(x) ≥ 4, for all x ∈(1,6), then:20204 September, Shift 1 · Q58
• Let f be any function continuous on [a, b] and twice differentiable on (a, b). If for all x ∈(a, b), f^′(x)>0 and f^′ ′(x)<0,…20209 January, Shift 1 · Q60
• Let S be the set of all functions f:[0,1] → R, which are continuous on [0,1] and differentiable on (0, 1). Then for every f in S,…20208 January, Shift 2 · Q59
• The value of c in the Lagrange's mean value theorem for the function f(x)=x^3-4 x^2+8 x+11, when x ∈[0,1] is:20207 January, Shift 2 · Q59
• Let the function, f:[-7,0] → R be continuous on [-7,0] and differentiable on (-7,0). If f(-7)=-3 and f^′(x) ≤ 2, for all x…20207 January, Shift 1 · Q59