For what choices of a,b,c if any , does the function
`f(x) = {:{(ax^2+bx+c,0lexle1),(bx-c,1lexle2),(c,x>2):}` become differentiable at x =1 andx=2?

For what values of 'a' and 'b' the function: f(x) = {:{(x^2,xlec),(ax+b,x>c):} is differentiable at x =c.

Discuss the continuity of the function: f(x) = {:{(1+x^2,0lexle1),(2-x,x>1):} at x =1

The function f(x)={:{(x+2,ifxlt-1),(x^(2),if-1lexle1),((x-2)^(2),ifxge1):}

Draw the graph of the function : f(x)= |1-x|+|1+x|, -2 lexle2 .

The function f(x)=(x^2-1)|x^2-3x+2|+cos(|x|) is differentiable not differentiable at (a)-1 (b)0 (c)1 (d)2

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

Find 'a' and 'b' if the function: f(x) = {:{((sinx)/x, -2lex<0),(a.2^x,0lexle1),(b+x,1< xle2):} is a continuous function on [-2,2]

Evaluate: underset(-2)overset(2)int(f(x) dx where f(x) = {:{(2x-1,-2lexle1),(3x-2,1lexle2)

Find the derivatives of the following at any point of their domains : f(x) = 1/(ax^2+bx+c) .

Examine the differentiability of the function 'f' defined by: f(x) = {:{(2x+3,if-3lex <-2),(x+1,if-2lex<0),(x+2,if0lexle1):}