I can not get these three problems. I tried and tried but nothing makes sense. If someone could walk me through it and explain them to me I would be very grateful.

1)Let $\displaystyle p$ and $\displaystyle q$ be real numbers and let $\displaystyle f$ be the function defined by

$\displaystyle f(x)$= $\displaystyle 1+2p(x-1)+(x-1)^2$, for x less than or equal to 1 and $\displaystyle qx+p$, for x greater than 1

(a) find the values of $\displaystyle q$, in terms of $\displaystyle p$, for which $\displaystyle f$ is continuous at $\displaystyle x=1$

(b) find the values of $\displaystyle p$ and $\displaystyle q$ for which $\displaystyle f$ is differentiable at $\displaystyle x=1$

(c) if $\displaystyle p$ and $\displaystyle q$ have the values determined in part (b), is second derivative $\displaystyle f$ a continuous function? Justify you answer.

6)Let $\displaystyle P(x)=x^4+ax^3+bx^2+cx+d$. The graph $\displaystyle y=P(x)$ is symmetric with respect to the Y-axis, has relative maximum at $\displaystyle (0,1)$, and has an absolute minimum at $\displaystyle (q, -3)$

a) determine the values $\displaystyle a, b, c, d$ and using these values write an expression for $\displaystyle P(x)$

b)Find all possible values of $\displaystyle q$

7)given the curve $\displaystyle x^2-xy+y^2=9$

(a) write a general expression for the slope of the curve.

(b) Find the coordinates of the points on the curve where the tangents are vertical.

(c) at the point $\displaystyle (0,3)$ find the change in the slope of the curve with respect to x.

Thank you everybody for all your help!