f(x) is both functions.. I dont know why the system didnt let me keep the spaces to show that
First off, stop misspelling "calculus".
Now, if a=2 and b=3, we have
f(x) = 2x^2 - 3x
f(1) = -1
But lim x->1- = |1-1| + 2 = 2
So, f is not continuous at x=1.
If f is to be continuous, it needs to be continuous at x=1. It is continuous everywhere else already.
So, ax^2 - bx must = 2 at x=1
a - b = 2
So, there are any number of parabolas which will make f continuous at x=1.
6x^2 - 4x
-3x^2 + 5x
Now, for f to be also differentiable, the slopes must match at x=1
The slope of |x-1| is -1 when approaching from the left.
ax^2 - (a-2)x must also have slope -1 at x=1
f'(x) = 2ax - (a-2)
f'(1) = 2a - a + 2 = -1
a = -3
f(x) = |x-1| + 2 for x<1
f(x) = -3x^2 + 5x for x>=1
is both continuous and differentiable everywhere.
AP Calculous - let f be the function defined by f(x)=3X^5 -5X^3 +2 a) on what ...
Calculous - let f be the function defined by |x-1|+2 for X<1 f(x)= ax^2-Bx, ...
Calculous - let f be the function defined by f(x)=12x^2/3 -4X a)find the ...
Calculous - the figure shows the graph of F', the derivative of a function f. ...
AP Calculous - A particle moves on the x ľaxis so that its position at any time...
calculous - 3.Given the function f defined by f(x)=2x^3-3x^2-12x+20 a.Find the ...
Calculus AP - 5.2 The Natural logarithmic function Differentiate the function ...
pre calc - The Identity Function The Squaring Function The Cubing Function The ...
AP Calc - For the function find the derivative of its inverse given a point on ...
AP Biology for Kate, etc. - To save your looking for these AP Biology sites, I ...