I've been trying to find what time, t gives the maximum altitude for this question. I've found the answer using derivative way however i'm taking a advanced functions course and the teacher won't allow the calculus way so is there another way to find the value of t that gives the maximum altitude from this equation:
h(t) = -16t^2 + 90t + 10 000
Alternatively, you could think of the graph of this function.
It's a negative parabola. Parabolas are symmetrical along their maxima or minima.
So the t co-ordinate you require will lie along the quadratic's line of symmetry. The way to find the line of symmetry is straightforward:
Put the function equal to 0 and solve, to find the t-intercepts.
This gives or
Not very nice.
The line of symmetry will lie exactly half-way between them:
This is the same result (approximately) that you'd get using calculus - for an exact answer, solve the quadratic exactly, leaving your answer in surd form - the surds should cancel and you get . Not very impressive, but heck - it works.