3
votes
3answers
126 views

Finding maximum value for a function

I was working on this question to find the following function's maximum value.Let $$y=f(x)={{(\sqrt{-3+4x-x^2}+4)}}^2 + (x-5)^2$$ where $$1 \le x \le 3$$.I have to find it's maximum value. I tried by ...
2
votes
1answer
62 views

Least value of $a$ for which at least one solution exists?

What is the least value of $a$ for which $$\frac{4}{\sin(x)}+\frac{1}{1-\sin(x)}=a$$ has atleast one solution in the interval $(0,\frac{\pi}{2})$? I first calculate $f'(x)$ and put it equal to $0$ to ...
3
votes
1answer
398 views

Finding coefficients of quadratic given one tangent and point on the curve

I am given a quadratic equation: $$ y = Ax^2 + Bx + C $$ that passes through $(1,3)$ and $(2,3)$, and a tangent to the curve is $x - y + 1 = 0$ at $(2.3)$. How do I find $A$, $B$, and $C$? The ...
3
votes
1answer
451 views

Given a cubic function, and its quadratic derivative- can I recover the cubic from quadratic?

Background: I'm trying to learn how to work with cubic and quadratic bezier splines for various drawing libraries, and working through how to approximate a cubic spline with a quadratic spline. It's ...