Find the solution of the following initial value...

Transcript

00:01 We want to solve the following initial value problem.

00:04 Second derivative of f equal negative 24x squared minus 6x minus 10.

00:11 The first derivative of f at 1 is negative 23, and f at 1 is negative 28.

00:22 So we have a second degree differential equation right here, and we have an initial value problem because we have, besides the differential equation, we have two conditions.

00:32 In this case we need two conditions because we have the second derivative of f appearing in the equation, so it's second order, and so we need conditions on the function and the derivatives, and the first derivative, sorry, at the same point, in this case x equals 1.

00:52 And we also notice that the differential equation right here is involving only x on the right hand side.

01:01 We have the second derivative of f at x equal a function of only x.

01:06 So we can solve this differential equation by simply integrating both sides of the equation in two steps.

01:14 So first, if the second derivative of f of x being equal to 24x squared minus 6x minus 10, then we can say that the integral of this, the the indefinite integral of the second derivative of f at x with respect to x is the integral of negative 24x squared minus 6x plus 10, sorry, minus 10 differential of x.

01:55 And when we calculate this, we notice is the first derivative of f equal, because the first derivative is a primitive for the second derivative, the first derivative differentiated gives us the second derivative...

Question

Find the solution of the following initial value problems.\ f'(x) = 8x - 7; f(0) = 5\ The solution to the initial value problem is f(x) = \boxed{ }

Question

Find the solution of the following initial value problems.\ f'(x) = 8x - 7; f(0) = 5\ The solution to the initial value problem is f(x) = \boxed{ }

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