Let f be twice differentiable and one-to-one on an open interval I . show that its inverse function g satisfies g"(x)=−f"(g(x))[f′(g(x))]3 Implicit Differentiation If we have an equation (not necessarily a function) relating ...
We have a twice differentiable function f such that:1. f′′(x)=−f(x)2. f′(x)=g(x) We also have a function defined as:h(x)=f(x)2+g(x)2 Step 2: Differentiate h(x)To find h′(x), we apply the chain rule:h′(x)=2f(x)f′(x)+2g(x)g′(x)Substituting f′(x...
Let f(x) be twice differentiablesuchthat f''(x)=-f(x), f' (x) = g(x), where f' (x) and f ''(x) represent the first and second derivatives of f(x), respectivel
Let h be a twice differentiable function, and let h(-4)=-3, h′(−4)=0 and h''(-4)=0. What occurs in the graph of h at the point (-4,-3) . A、 (-4,3) is a minimum point B、(-4,-3) is a maximum point C、There’s not enough information to tell D、 (-4,-
Let h be a twice differentiable function, andeth(-4)=-3,h'(-4)=0,andh'(-4)=0What occurs in the graph of h at the point (-4, -3)? 相关知识点: 试题来源: 解析 ∵h'(-4)=0 H—4)=0 ∴at(-4,-3)tanθmph has a point o f(lng)f(t)0h ...
A. Suppose \int\limits_0^1 f(t) dt = 3. Find \int\limits_1^{1.5} f(3 - 2t) dt. B. Let f be twice differentiable with f(0) = 6, f(1) = 5, and f'(1) = 2. Find \int\limits_0^1 xf''(x) dx. Suppose f(x) is different...
If g is the function defined by g(x) = (x^2 +1)/f(x), what is the value of g'(2) - 8/9 ∫1→-1 (x^2-x)/x dx is -2 The table above gives selected values for the differentiable function f. In which of the following intervals must there be a number c such that f'...
h be a twice differentiable function, and leth(-4)=-3,h′(−4)=0 andh''(-4)=0. What occurs in the graph ofh at the point (-4,-3) . A. (-4,3) is a minimum point B. (-4,-3) is a maximum point C. There’s not enough information to tell D. (-4,-3) is a ...
9. The function f is twice differentiable, and the graph of f has no points of inflection. If f(6) = 3, f'(6) = -1/2, and f''(6) = -2, which of the following could be the value of f(7)? A) 2 10. A function f has Maclaurin series given by 1 + x^2/2! +x^4...
Let f be twice differentiable with f(0) = 8, f(1) = 2, and f'(1) = 7. Evaluate the integral \int_0^1 x f''(x) dx The functions f and g are integrable and \int_2^4 f(x)dx = -6, \int_2^7 f (x) dx = -4, and \int_2...